Question: Which of the following numbers is a factor of 189? ${4,8,9,12,14}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $189$ by each of our answer choices. $189 \div 4 = 47\text{ R }1$ $189 \div 8 = 23\text{ R }5$ $189 \div 9 = 21$ $189 \div 12 = 15\text{ R }9$ $189 \div 14 = 13\text{ R }7$ The only answer choice that divides into $189$ with no remainder is $9$ $ 21$ $9$ $189$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $189$ $189 = 3\times3\times3\times7 9 = 3\times3$ Therefore the only factor of $189$ out of our choices is $9$. We can say that $189$ is divisible by $9$.